导数无界的间断映射的统计性质
Statistical properties of intermittent maps with unbounded derivative
摘要：
本文研究了一类Lorenz型区间圆映射的遍历性和统计性，其中存在中立不动点和具有无界导数的点。这些地图以前已经在物理学文献中进行了研究。我们证明，特别是相关多项式衰减，并认为适当的极限定理（收敛到稳定的法律或中心极限定理）举行霍尔德连续可观。我们还证明了收益率和首中时服从极限指数分布。
英文摘要：
We study the ergodic and statistical properties of a class of maps of the circle and of the interval of Lorenz type which present indifferent fixed points and points with unbounded derivative. These maps have been previously investigated in the physics literature. We prove in particular that correlations decay polynomially, and that suitable Limit Theorems (convergence to Stable Laws or Central Limit Theorem) hold for Hölder continuous observables. We moreover show that the return and hitting times are in the limit exponentially distributed.
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